Solving Polynomial Equations

Front

What is a polynomial equation?

Back

A polynomial equation is an equation that involves a polynomial expression, which is a mathematical expression consisting of variables raised to whole number powers and coefficients.

Front

What is the degree of a polynomial?

Back

The degree of a polynomial is the highest power of the variable in the polynomial expression.

Front

What are the roots of a polynomial?

Back

The roots of a polynomial are the values of the variable that make the polynomial equal to zero.

Front

What does it mean for a root to have multiplicity?

Back

Multiplicity refers to the number of times a particular root appears in the factorization of a polynomial.

Front

How do you factor a difference of squares?

Back

A difference of squares can be factored using the formula a^2 - b^2 = (a - b)(a + b).

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What is the Factor Theorem?

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The Factor Theorem states that if f(c) = 0 for a polynomial f(x), then (x - c) is a factor of f(x).

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How do you determine if a polynomial has real roots?

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You can determine if a polynomial has real roots by analyzing its discriminant or using the Rational Root Theorem.

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What is synthetic division?

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Synthetic division is a simplified method of dividing a polynomial by a linear factor, which is faster than long division.

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What is the Remainder Theorem?

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The Remainder Theorem states that the remainder of the division of a polynomial f(x) by (x - c) is equal to f(c).

Front

Solve the polynomial equation: (x^2 - 9) = 0

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x = 3, -3